Update documentation for floating-point precision and determinant calculations (numpy#27602)

* Update basics.types.rst: Clarify determinant precision handling

This update adds clarification to the section on numerical data types regarding the precision of matrix determinants in NumPy. A note has been included explaining that results close to zero, such as those from the determinant of the matrix np.array([[5,5,6],[7,7,5],[4,4,8]]), can appear as very small negative numbers due to floating-point precision issues.

Additionally, a reference to the `np.isclose()` function has been added to guide users on checking if a value is close to zero, which can help mitigate confusion regarding the expected result of zero for certain matrix determinants.

* Update basics.types.rst: Clarify determinant precision handling

This update adds clarification to the section on numerical data types regarding the precision of matrix determinants in NumPy. A note has been included explaining that results close to zero, such as those from the determinant of the matrix np.array([[5,5,6],[7,7,5],[4,4,8]]), can appear as very small negative numbers due to floating-point precision issues.

Additionally, a reference to the `np.isclose()` function has been added to guide users on checking if a value is close to zero, which can help mitigate confusion regarding the expected result of zero for certain matrix determinants.

* Update basics.types.rst: Clarify determinant precision handling

This update adds clarification to the section on numerical data types regarding the precision of matrix determinants in NumPy. A note has been included explaining that results close to zero, such as those from the determinant of the matrix np.array([[5,5,6],[7,7,5],[4,4,8]]), can appear as very small negative numbers due to floating-point precision issues.

Additionally, a reference to the `np.isclose()` function has been added to guide users on checking if a value is close to zero, which can help mitigate confusion regarding the expected result of zero for certain matrix determinants.

* Update basics.types.rst: Clarify determinant precision handling

This update adds clarification to the section on numerical data types regarding the precision of matrix determinants in NumPy. A note has been included explaining that results close to zero, such as those from the determinant of the matrix np.array([[5,5,6],[7,7,5],[4,4,8]]), can appear as very small negative numbers due to floating-point precision issues.

Additionally, a reference to the `np.isclose()` function has been added to guide users on checking if a value is close to zero, which can help mitigate confusion regarding the expected result of zero for certain matrix determinants.

* Update basics.types.rst: Clarify determinant precision handling

This update adds clarification to the section on numerical data types regarding the precision of matrix determinants in NumPy. A note has been included explaining that results close to zero, such as those from the determinant of the matrix np.array([[5,5,6],[7,7,5],[4,4,8]]), can appear as very small negative numbers due to floating-point precision issues.

Additionally, a reference to the `np.isclose()` function has been added to guide users on checking if a value is close to zero, which can help mitigate confusion regarding the expected result of zero for certain matrix determinants.

* Update basics.types.rst: Clarify determinant precision handling

This update adds clarification to the section on numerical data types regarding the precision of matrix determinants in NumPy. A note has been included explaining that results close to zero, such as those from the determinant of the matrix np.array([[5,5,6],[7,7,5],[4,4,8]]), can appear as very small negative numbers due to floating-point precision issues.

Additionally, a reference to the `np.isclose()` function has been added to guide users on checking if a value is close to zero, which can help mitigate confusion regarding the expected result of zero for certain matrix determinants.

* Update basics.types.rst: Clarify determinant precision handling

This update adds clarification to the section on numerical data types regarding the precision of matrix determinants in NumPy. A note has been included explaining that results close to zero, such as those from the determinant of the matrix np.array([[5,5,6],[7,7,5],[4,4,8]]), can appear as very small negative numbers due to floating-point precision issues.

Additionally, a reference to the `np.isclose()` function has been added to guide users on checking if a value is close to zero, which can help mitigate confusion regarding the expected result of zero for certain matrix determinants.

* Updating basics.types.rst: Clarify precision handling and link to floating point arithmetic reference. [skip azp][skip actions][skip cirrus]

Updating basics.types.rst:

- Reflowed text to adhere to the 88-column limit for better readability.
- Added a link to an external resource for further information on floating-point arithmetic.

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* Updating basics.types.rst: Clarify precision handling and link to floating point arithmetic reference. [skip azp][skip actions][skip cirrus]

Updating basics.types.rst:

- Reflowed text to adhere to the 88-column limit for better readability.
- Added a link to an external resource for further information on floating-point arithmetic.

[skip azp][skip actions][skip cirrus]

* Update basics.types.rst: Added a new section "Floating-point precision". [skip azp][skip actions][skip cirrus]

- Moved the floating-point precision details into a new dedicated section titled "Floating Point Precision" for better discoverability.
- Reflowed text to adhere to the 88-column limit for readability.
- Added a link to an external resource on floating-point arithmetic for users seeking more detailed information.

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* Update doc/source/user/basics.types.rst: Update floating-point precision section for clarity.[skip azp][skip actions][skip cirrus]

- Updated the description of floating-point behavior for improved clarity.
- Changed phrasing from "a known behavior of floating-point operations in numerical libraries" to "a behavior common to all frameworks that use floating point arithmetic."

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Co-authored-by: Jake Vanderplas <[email protected]>

* Update floating-point precision section: Replaced np.isclose() with np.linalg.cond()

- Replaced the usage of np.isclose() with np.linalg.cond() to assess matrix stability.
- Cond function provides a more accurate measure of how close a matrix is to being singular.

* Update floating-point precision section: Replaced np.isclose() with np.linalg.cond() [skip azp][skip actions][skip cirrus]

- Replaced the usage of np.isclose() with np.linalg.cond() to assess matrix stability.
- Cond function provides a more accurate measure of how close a matrix is to being singular.
[skip azp][skip actions][skip cirrus]

* Simplified floating-point precision example by removing determinant and adding basic arithmetic case. [skip azp][skip actions][skip cirrus]

- Removed the matrix determinant example to keep the focus on the general floating-point arithmetic issue.
- Replaced with an example that illustrates floating-point precision in basic arithmetic.
- Added explanation to make the topic more accessible for new users.
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---------

Co-authored-by: Jake Vanderplas <[email protected]>

Author: amitsubhashchejara

doc/source/user/basics.types.rst

@@ -342,6 +342,30 @@ range of possible values.
     >>> np.power(100, 100, dtype=np.float64)
     1e+200
 
+Floating point precision
+========================
+
+Many functions in NumPy, especially those in `numpy.linalg`, involve floating-point
+arithmetic, which can introduce small inaccuracies due to the way computers 
+represent decimal numbers. For instance, when performing basic arithmetic operations 
+involving floating-point numbers:
+
+    >>> 0.3 - 0.2 - 0.1  # This does not equal 0 due to floating-point precision
+    -2.7755575615628914e-17
+
+To handle such cases, it's advisable to use functions like `np.isclose` to compare 
+values, rather than checking for exact equality:
+
+    >>> np.isclose(0.3 - 0.2 - 0.1, 0, rtol=1e-05)  # Check for closeness to 0
+    True
+
+In this example, `np.isclose` accounts for the minor inaccuracies that occur in 
+floating-point calculations by applying a relative tolerance, ensuring that results
+within a small threshold are considered close.
+
+For information about precision in calculations, see `Floating-Point Arithmetic <https://docs.oracle.com/cd/E19957-01/806-3568/ncg_goldberg.html>`_.
+
+
 Extended precision
 ==================